Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Possibility of a Two-Component Tomonaga-Luttinger Liquid in Frustrated Integer-Spin Tubes

Masahiro Sato

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Abstract. Uniform-field effects for frustrated odd-leg integer-spin tubes (cylinder type spin systems) are investigated in the weak interchain-coupling regime. We predict that, as the field exceeds the spin gap, a two-component Tomonaga-Luttinger liquid (TLL) appears due to the condensation of the doubly degenerate lowest magnons. Furthermore, it is argued that when the uniform field is so strong that the second lowest magnons are also condensed, the two-component TLL is destroyed and a new one-component TLL emerges. This quantum phase transition may be detected as a magnetization cusp. Keywords: integer-spin tube, frustration, Tomonaga-Luttinger liquid, magnetization cusp, nonlinear sigma model, bosonization PACS: 75.10.Jm, 75.40.Cx, 75.50.Ee In one-dimensional (1D) gapped isotropic spin systems, a uniform magnetic field, which causes the rotation symmetry to reduce to a U(1) one, generally removes the gap and induces a magnon-condensed phase regarded as a Tomonaga-Luttinger liquid (TLL) [1] with central charge c = 1. Zamolodchikov’s c theorem [2] actually predicts that a c = 1 TLL state tends to occur in U(1) symmetric 1D systems. However, frustration often breaks such conventional scenarios. In this short paper, we focus on the field-induced critical phases in frustrated integer-spin tubes, and discuss the possibility of the existence of an unconventional two-component TLL (we call this c = 1 + 1 state in this paper) and a quantum phase transition. Here, the tube means a ladder with a periodic boundary condition along the interchain (rung) direction. For more details, refer to Ref. [3]. The N(finite)-leg spin tube Hamiltonian is given by

Related papers

Possibility of a Two-Component Tomonaga-Luttinger Liquid in Frustrated Integer-Spin Tubes

Masahiro Sato

Uniform‐field effects for frustrated odd‐leg integer‐spin tubes (cylinder type spin systems) are investigated in the weak interchain‐coupling regime. We predict that, as the field exceeds the spin gap, a two‐component Tomonaga‐Luttinger liquid (TLL) appears due to the condensation of the doubly degenerate lowest magnons. Furthermore, it is argued that when the uniform field is so strong that the second lowest magnons are also condensed, the two‐component TLL is destroyed and a new one‐component TLL emerges. This quantum phase transition may be detected as a magnetization cusp.

arXiv:cond-mat/0511024•AIP conference proceedings•Jan 1, 2006•0 citations

Coexistence of vector chiral order and Tomonaga-Luttinger liquid in the frustrated three-leg spin tube in a magnetic field

Masahiro Sato

The frustrated three-leg antiferromagnetic spin-$\frac{1}{2}$ tube with a weak interchain coupling in a magnetic field is investigated by means of Abelian bosonization techniques. It is clearly shown that a vector chiral long-range order and a one-component Tomonaga-Luttinger liquid coexist in a wide magnetic-field region from a state with a small magnetization to a nearly saturated one. The chiral order is predicted to still survive in the intermediate plateau state. We further predict that (even) when the strength of one bond in the three rung couplings is decreased (increased), an Ising-type quantum phase transition takes place and the chirality vanishes (no singular phenomena occur and the chiral order is maintained). Even without magnetic fields, the chiral order would also be present if the spin tube possesses easy-plane anisotropy.

arXiv:cond-mat/0612165•Physical Review B•May 4, 2007•29 citations

Double zigzag spin chain in a strong magnetic field close to saturation

I. T. Shyiko, Ian P. McCulloch, J.V. Gumenjuk-Sichevska +1 more

We study the ground state phase diagram of a frustrated spin tube in a strong external magnetic field. This model can be viewed as two coupled zigzag spin chains, or as a two-leg spin ladder with frustrating next-nearest-neighbor couplings along the legs, and its study is motivated by the physics of such materials as sulfolane-${\mathrm{Cu}}_{2}{\mathrm{Cl}}_{4}$ and ${\mathrm{BiCu}}_{2}{\mathrm{PO}}_{6}$. In magnetic fields right below the saturation, the system can be effectively represented as a dilute gas of two species of bosonic quasiparticles that correspond to magnons with inequivalent incommensurate momenta at two degenerate minima of the magnon dispersion. Using the method previously proposed and tested for frustrated spin chains, we calculate effective interactions in this two-component Bose gas. On this basis, we establish the phase diagram of nearly saturated frustrated spin tube, which is shown to include the two-component Luttinger liquid, two types of vector chiral phases, and phases whose physics is determined by the presence of bound magnons. We study the phase diagram of the model numerically by means of the density matrix renormalization group technique, and find a good agreement with our analytical predictions.

arXiv:1303.6662•Physical Review B•Jul 8, 2013•13 citations

Spontaneously magnetized Tomonaga-Luttinger liquid in frustrated quantum antiferromagnets

Shunsuke C. Furuya, Thierry Giamarchi

We develop a theory of spontaneously magnetized Tomonaga-Luttinger (TLL) liquid in geometrically frustrated quasi-one-dimensional quantum magnets by taking an $S=1/2$ ferrimagnet on a union-jack lattice as an example. We show that a strong frustration leads to a spontaneous magnetization because of the ferrimagnetic nature of lattice. Due to the ferrimagnetic order, the local magnetization has an incommensurate oscillation with the position. We show that the spontaneously magnetized TLL is smoothly connected to the existence of a Nambu-Goldstone boson in the canted ferrimagnetic phase of a two-dimensional frustrated antiferromagnet.

arXiv:1403.1513•Physical Review B•May 27, 2014•32 citations

Tomonaga-Luttinger liquid theory for one-dimensional attractive Fermi gases

Anonymous, Yu-Hao Yeh, Aashish Kafle +4 more

The one-dimensional (1D) Yang-Gaudin model--an integrable $δ$-function interacting Fermi gas, serves as a paradigm in quantum many-body physics, encompassing phenomena from spin-charge separation to the Luther-Emery liquid. However, a consistent description of the Luther-Emery liquid and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like pairing states in the 1D attractive Fermi gas remains elusive. In this work, we develop a universal Tomonaga-Luttinger liquid (TLL) theory to describe the FFLO state both for the case of weak and strong binding between fermions of opposite spins. We rigorously derive a low-energy effective Hamiltonian using bosonization, revealing the emergence of a two-component TLL: one exhibiting spin-charge coupling in the weak binding regime, and another featuring charge-charge separation in the strong binding regime. For the weak binding regime, we further derive renormalization-group equations for the sine-Gordon term in the spin sector and show that this term undergoes a relevant-irrelevant phase transition driven by the magnetic field. We further analyze the dynamical correlation functions of the FFLO pairing state based on the effective Hamiltonian we constructed. Finally, we discuss experiments using ultracold atoms to elucidate the Luther-Emery liquid behavior and the subtle phenomena of spin-charge coupling and charge-charge separation.

arXiv:2603.13958•Physical Review A•Sep 9, 2026•0 citations

Exotic Quantum Phase Transitions in Spin Nanotubes

Tôru Sakai, Masahiro Sato, Kouichi Okunishi +2 more

Recently some quantum spin systems on tube lattices, so called spin nanotubes, have been synthesized. They are expected to be interesting low-dimensional systems like the carbon nanotubes. As the first step of theoretical study on the spin nanotube, we investigate the S=1/2 three-leg spin tube, which is the simplest one, using the numerical exact diagonalization and the finite-size scaling analysis. In our previous works the quantum phase transition between the spin-gap and gapless phases was revealed to occur due to the asymmetric lattice distortion. In addition the transition between the magnetization plateau and gapless phases at 1/3 of the saturation magnetization induced by the same distortion. Recently we found that the Tomonaga-Luttinger liquid is realized in the 1/3 magnetization plateau phase for the symmetric three-leg spin tube.

Journal of Physics Conference Series•Dec 17, 2012•1 citation
Abstract. Uniform-field effects for frustrated odd-leg integer-spin tubes (cylinder type spin systems) are investigated in the weak interchain-coupling regime. We predict that, as the field exceeds the spin gap, a two-component Tomonaga-Luttinger liquid (TLL) appears due to the condensation of the doubly degenerate lowest magnons. Furthermore, it is argued that when the uniform field is so strong that the second lowest magnons are also condensed, the two-component TLL is destroyed and a new one-component TLL emerges. This quantum phase transition may be detected as a magnetization cusp. Keywords: integer-spin tube, frustration, Tomonaga-Luttinger liquid, magnetization cusp, nonlinear sigma model, bosonization PACS: 75.10.Jm, 75.40.Cx, 75.50.Ee In one-dimensional (1D) gapped isotropic spin systems, a uniform magnetic field, which causes the rotation symmetry to reduce to a U(1) one, generally removes the gap and induces a magnon-condensed phase regarded as a Tomonaga-Luttinger liquid (TLL) [1] with central charge c = 1. Zamolodchikov’s c theorem [2] actually predicts that a c = 1 TLL state tends to occur in U(1) symmetric 1D systems. However, frustration often breaks such conventional scenarios. In this short paper, we focus on the field-induced critical phases in frustrated integer-spin tubes, and discuss the possibility of the existence of an unconventional two-component TLL (we call this c = 1 + 1 state in this paper) and a quantum phase transition. Here, the tube means a ladder with a periodic boundary condition along the interchain (rung) direction. For more details, refer to Ref. [3]. The N(finite)-leg spin tube Hamiltonian is given by
Uniform‐field effects for frustrated odd‐leg integer‐spin tubes (cylinder type spin systems) are investigated in the weak interchain‐coupling regime. We predict that, as the field exceeds the spin gap, a two‐component Tomonaga‐Luttinger liquid (TLL) appears due to the condensation of the doubly degenerate lowest magnons. Furthermore, it is argued that when the uniform field is so strong that the second lowest magnons are also condensed, the two‐component TLL is destroyed and a new one‐component TLL emerges. This quantum phase transition may be detected as a magnetization cusp.
The frustrated three-leg antiferromagnetic spin-12\frac{1}{2}21​ tube with a weak interchain coupling in a magnetic field is investigated by means of Abelian bosonization techniques. It is clearly shown that a vector chiral long-range order and a one-component Tomonaga-Luttinger liquid coexist in a wide magnetic-field region from a state with a small magnetization to a nearly saturated one. The chiral order is predicted to still survive in the intermediate plateau state. We further predict that (even) when the strength of one bond in the three rung couplings is decreased (increased), an Ising-type quantum phase transition takes place and the chirality vanishes (no singular phenomena occur and the chiral order is maintained). Even without magnetic fields, the chiral order would also be present if the spin tube possesses easy-plane anisotropy.
We study the ground state phase diagram of a frustrated spin tube in a strong external magnetic field. This model can be viewed as two coupled zigzag spin chains, or as a two-leg spin ladder with frustrating next-nearest-neighbor couplings along the legs, and its study is motivated by the physics of such materials as sulfolane-Cu2Cl4{\mathrm{Cu}}_{2}{\mathrm{Cl}}_{4}Cu2​Cl4​ and BiCu2PO6{\mathrm{BiCu}}_{2}{\mathrm{PO}}_{6}BiCu2​PO6​. In magnetic fields right below the saturation, the system can be effectively represented as a dilute gas of two species of bosonic quasiparticles that correspond to magnons with inequivalent incommensurate momenta at two degenerate minima of the magnon dispersion. Using the method previously proposed and tested for frustrated spin chains, we calculate effective interactions in this two-component Bose gas. On this basis, we establish the phase diagram of nearly saturated frustrated spin tube, which is shown to include the two-component Luttinger liquid, two types of vector chiral phases, and phases whose physics is determined by the presence of bound magnons. We study the phase diagram of the model numerically by means of the density matrix renormalization group technique, and find a good agreement with our analytical predictions.
We develop a theory of spontaneously magnetized Tomonaga-Luttinger (TLL) liquid in geometrically frustrated quasi-one-dimensional quantum magnets by taking an S=1/2S=1/2S=1/2 ferrimagnet on a union-jack lattice as an example. We show that a strong frustration leads to a spontaneous magnetization because of the ferrimagnetic nature of lattice. Due to the ferrimagnetic order, the local magnetization has an incommensurate oscillation with the position. We show that the spontaneously magnetized TLL is smoothly connected to the existence of a Nambu-Goldstone boson in the canted ferrimagnetic phase of a two-dimensional frustrated antiferromagnet.
The one-dimensional (1D) Yang-Gaudin model--an integrable δδδ-function interacting Fermi gas, serves as a paradigm in quantum many-body physics, encompassing phenomena from spin-charge separation to the Luther-Emery liquid. However, a consistent description of the Luther-Emery liquid and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like pairing states in the 1D attractive Fermi gas remains elusive. In this work, we develop a universal Tomonaga-Luttinger liquid (TLL) theory to describe the FFLO state both for the case of weak and strong binding between fermions of opposite spins. We rigorously derive a low-energy effective Hamiltonian using bosonization, revealing the emergence of a two-component TLL: one exhibiting spin-charge coupling in the weak binding regime, and another featuring charge-charge separation in the strong binding regime. For the weak binding regime, we further derive renormalization-group equations for the sine-Gordon term in the spin sector and show that this term undergoes a relevant-irrelevant phase transition driven by the magnetic field. We further analyze the dynamical correlation functions of the FFLO pairing state based on the effective Hamiltonian we constructed. Finally, we discuss experiments using ultracold atoms to elucidate the Luther-Emery liquid behavior and the subtle phenomena of spin-charge coupling and charge-charge separation.
Recently some quantum spin systems on tube lattices, so called spin nanotubes, have been synthesized. They are expected to be interesting low-dimensional systems like the carbon nanotubes. As the first step of theoretical study on the spin nanotube, we investigate the S=1/2 three-leg spin tube, which is the simplest one, using the numerical exact diagonalization and the finite-size scaling analysis. In our previous works the quantum phase transition between the spin-gap and gapless phases was revealed to occur due to the asymmetric lattice distortion. In addition the transition between the magnetization plateau and gapless phases at 1/3 of the saturation magnetization induced by the same distortion. Recently we found that the Tomonaga-Luttinger liquid is realized in the 1/3 magnetization plateau phase for the symmetric three-leg spin tube.